Multistep DBT and regular rational extensions of the isotonic oscillator

  title={Multistep DBT and regular rational extensions of the isotonic oscillator},
  author={Yves Grandati},
  journal={arXiv: Mathematical Physics},
  • Y. Grandati
  • Published 23 August 2011
  • Mathematics
  • arXiv: Mathematical Physics

Rational extensions of solvable potentials and exceptional orthogonal polynomials

We present a generalized SUSY QM partnership in which the DBT are built on the excited states Riccati-Schrödinger (RS) functions regularized via specific discrete symmetries of translationally shape

Disconjugacy, regularity of multi-indexed rationally extended potentials, and Laguerre exceptional polynomials

The power of the disconjugacy properties of second-order differential equations of Schrodinger type to check the regularity of rationally extended quantum potentials connected with exceptional

New families of superintegrable systems from Hermite and Laguerre exceptional orthogonal polynomials

In recent years, many exceptional orthogonal polynomials (EOP) were introduced and used to construct new families of 1D exactly solvable quantum potentials, some of which are shape invariant. In this

Novel enlarged shape invariance property and exactly solvable rational extensions of the Rosen-Morse II and Eckart potentials

The existence of a novel enlarged shape invariance property valid for some ratio- nal extensions of shape-invariant conventional potentials, first pointed out in the case of the Morse potential, is

Comments on the generalized SUSY QM partnership for Darboux–Pöschl–Teller potential and exceptional Jacobi polynomials

A recently proposed scheme to generate the rational extensions of translationally shape-invariant potentials is applied to the trigonometric Darboux–Pöschl–Teller potential. It allows one in

Cyclic Maya diagrams and rational solutions of higher order Painlevé systems

This paper focuses on the construction of rational solutions for the A2n ‐Painlevé system, also called the Noumi‐Yamada system, which are considered the higher order generalizations of PIV. In this

Two-step rational extensions of the harmonic oscillator: exceptional orthogonal polynomials and ladder operators

The type III Hermite Xm exceptional orthogonal polynomial family is generalized to a double-indexed one Xm1,m2?> (with m1 even and m2 odd such that m2 > m1) and the corresponding rational extensions


A previous study of exactly solvable rationally-extended radial oscillator potentials and corresponding Laguerre exceptional orthogonal polynomials carried out in second-order supersymmetric quantum

Rational extensions of the trigonometric Darboux-Pöschl-Teller potential based on para-Jacobi polynomials

The possibility for the Jacobi equation to admit, in some cases, general solutions that are polynomials has been recently highlighted by Calogero and Yi, who termed them para-Jacobi polynomials. Such



Solvable rational extensions of the isotonic oscillator

Solvable Rational Potentials and Exceptional Orthogonal Polynomials in Supersymmetric Quantum Mechanics

New exactly solvable rationally-extended radial oscillator and Scarf I potentials are generated by using a constructive supersymmetric quantum mechanical method based on a reparametrization of the

Exceptional Laguerre and Jacobi polynomials and the corresponding potentials through Darboux–Crum transformations

A simple derivation is presented of the four families of infinitely many shape-invariant Hamiltonians corresponding to the exceptional Laguerre and Jacobi polynomials. The Darboux–Crum

Infinitely many shape-invariant potentials and cubic identities of the Laguerre and Jacobi polynomials

We provide analytic proofs for the shape invariance of the recently discovered [Odake and Sasaki, Phys. Lett. B 679, 414 (2009)] two families of infinitely many exactly solvable one-dimensional

Exceptional orthogonal polynomials, exactly solvable potentials and supersymmetry

We construct two new exactly solvable potentials giving rise to bound-state solutions to the Schrödinger equation, which can be written in terms of the recently introduced Laguerre- or Jacobi-type X1

Higher-order SUSY, exactly solvable potentials, and exceptional orthogonal polynomials

Exactly solvable rationally-extended radial oscillator potentials, whose wavefunctions can be expressed in terms of Laguerre-type exceptional orthogonal polynomials, are constructed in the framework

Solvable rational extensions of the Morse and Kepler-Coulomb potentials

We show that it is possible to generate an infinite set of solvable rational extensions from every exceptional first category translationally shape invariant potential. This is made by using

Solvable rational extension of translationally shape invariant potentials

Combining recent results on rational solutions of the Riccati-Schr\"odinger equations for shape invariant potentials to the scheme developed by Fellows and Smith in the case of the one dimensional

Zeros of the Exceptional Laguerre and Jacobi Polynomials

An interesting discovery in the last two years in the field of mathematical physics has been the exceptional 𝑋l Laguerre and Jacobi polynomials. Unlike the well-known classical orthogonal